A rate dependent tension–torsion constitutive model for superelastic nitinol under non-proportional loading; a departure from von Mises equivalency

In this work, a modified 3D model is presented to capture the multi-axial behavior of superelastic shape memory alloys (SMAs) under quasi-static isothermal or dynamic loading conditions. General experimental based equivalent stress and strain terms are introduced and improved flow rule and transformation surfaces are presented. The 3D constitutive equations are found for both isothermal and dynamic loading states. An extended experimental study is conducted on NiTi thin walled tubes to investigate the performance of the model. The proposed approach is shown to be able to capture the SMA response better than the original model in tension‐torsion loading conditions.

[1]  S. Nemat-Nasser,et al.  Superelastic and cyclic response of NiTi SMA at various strain rates and temperatures , 2006 .

[2]  P. Papadopoulos,et al.  An experimental study of the superelastic effect in a shape-memory Nitinol alloy under biaxial loading , 2003 .

[3]  O. Borisov.  Conformations of Star-Branched Polyelectrolytes , 1996 .

[4]  Reginald DesRoches,et al.  Rate-dependent Thermo-mechanical Modelling of Superelastic Shape-memory Alloys for Seismic Applications , 2008 .

[5]  Siewert J Marrink,et al.  Molecular dynamics simulations of hydrophilic pores in lipid bilayers. , 2004, Biophysical journal.

[6]  Sylvain Calloch,et al.  A 3D super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings , 2009 .

[7]  N. Colgan,et al.  Applying DTI white matter orientations to finite element head models to examine diffuse TBI under high rotational accelerations. , 2010, Progress in biophysics and molecular biology.

[8]  R. Mehrabi,et al.  3D phenomenological constitutive modeling of shape memory alloys based on microplane theory , 2013 .

[9]  Christian Licht,et al.  Thermomechanical couplings and pseudoelasticity of shape memory alloys , 1998 .

[10]  C. Rinaldi,et al.  Molecular dynamics simulations of rupture in lipid bilayers , 2010, Experimental biology and medicine.

[11]  Jun Liao,et al.  Coupled experiment/finite element analysis on the mechanical response of porcine brain under high strain rates. , 2011, Journal of the mechanical behavior of biomedical materials.

[12]  R. Mirzaeifar,et al.  Exact solutions for pure torsion of shape memory alloy circular bars , 2010 .

[13]  O. Bruhns,et al.  On the viscous and strain rate dependent behavior of polycrystalline NiTi , 2008 .

[14]  D. Lagoudas.  Shape memory alloys : modeling and engineering applications , 2008 .

[15]  Christian Lexcellent,et al.  Mechanical Behavior of a Cu-Al-Be Shape Memory Alloy Under Multiaxial Proportional and Nonproportional Loadings , 2002 .

[16]  Michelle C LaPlaca,et al.  Mechanical stretch to neurons results in a strain rate and magnitude-dependent increase in plasma membrane permeability. , 2003, Journal of neurotrauma.

[17]  D Needham,et al.  Elastic deformation and failure of lipid bilayer membranes containing cholesterol. , 1990, Biophysical journal.

[18]  Evan Evans,et al.  Dynamic tension spectroscopy and strength of biomembranes. , 2003, Biophysical journal.

[19]  M. Elahinia,et al.  Modifying the torque–angle behavior of rotary shape memory alloy actuators through axial loading: A semi-analytical study of combined tension–torsion behavior , 2013 .

[20]  Kevin W Eliceiri,et al.  NIH Image to ImageJ: 25 years of image analysis , 2012, Nature Methods.

[21]  Otto T. Bruhns,et al.  Path dependence and multiaxial behavior of a polycrystalline NiTi alloy within the pseudoelastic and pseudoplastic temperature regimes , 2009 .

[22]  F. Falk,et al.  Pseudoelastic stress-strain curves of polycrystalline shape memory alloys calculated from single crystal data , 1989 .

[23]  T. Tadaki,et al.  Shape Memory Alloys , 2002 .

[24]  Masataka Tokuda,et al.  Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces , 1995 .

[25]  Orsolya Farkas,et al.  Cellular and subcellular change evoked by diffuse traumatic brain injury: a complex web of change extending far beyond focal damage. , 2007, Progress in brain research.

[26]  M. Shiga,et al.  Rapid estimation of elastic constants by molecular dynamics simulation under constant stress , 2004 .

[27]  E. Evans,et al.  Kinetics of hole nucleation in biomembrane rupture , 2011, New journal of physics.

[28]  Reginald DesRoches,et al.  Continuum Mechanics and Thermodynamics Manuscript No. Analysis of the Rate-dependent Coupled Thermo- Mechanical Response of Shape Memory Alloy Bars and Wires in Tension , 2022 .

[29]  Mojtaba Mahzoon,et al.  Modeling of the cyclic thermomechanical response of SMA wires at different strain rates , 2007 .

[30]  A. Stukowski.  Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool , 2009 .

[31]  Y. Chemisky,et al.  Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation , 2011 .

[32]  R.J.H. Cloots,et al.  Biomechanics of Traumatic Brain Injury: Influences of the Morphologic Heterogeneities of the Cerebral Cortex , 2008, Annals of Biomedical Engineering.

[33]  K. Barbee,et al.  Mechanically-induced membrane poration causes axonal beading and localized cytoskeletal damage , 2008, Experimental Neurology.

[34]  Craig A. Rogers,et al.  One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials , 1990 .

[35]  L. G. Machado,et al.  Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys , 2012 .

[36]  S. Padula,et al.  A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions , 2011 .

[37]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[38]  S. Wada,et al.  Molecular dynamics simulations of pore formation dynamics during the rupture process of a phospholipid bilayer caused by high-speed equibiaxial stretching. , 2011, Journal of biomechanics.

[39]  Alexander D. MacKerell,et al.  Update of the CHARMM all-atom additive force field for lipids: validation on six lipid types. , 2010, The journal of physical chemistry. B.

[40]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[41]  L. Brinson.  One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable , 1993 .

[42]  Shigenori Kobayashi,et al.  Thermomechanics of Transformation Pseudoelasticity and Shape Memory Effect in Alloys , 1986 .

[43]  J. Povlishock,et al.  Mechanoporation Induced by Diffuse Traumatic Brain Injury: An Irreversible or Reversible Response to Injury? , 2006, The Journal of Neuroscience.

[44]  D. Lagoudas,et al.  Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms , 2000 .

[45]  Bernard R. Brooks,et al.  Computer simulation of liquid/liquid interfaces. I. Theory and application to octane/water , 1995 .

[46]  Alessandro Reali,et al.  A 3-D phenomenological constitutive model for shape memory alloys under multiaxial loadings , 2010 .

[47]  L. Brinson,et al.  A three-dimensional phenomenological model for martensite reorientation in shape memory alloys , 2007 .

[48]  P. Šittner,et al.  On Transformation Pathways of General Stress Controlled Thermoelastic Martensitic Transformation in Shape Memory Alloys , 1996 .

[49]  Shanglian Huang,et al.  A comprehensive description for shape memory alloys with a two-phase constitutive model , 2001 .

[50]  H. A. Levy,et al.  Liquid Water: Molecular Correlation Functions from X‐Ray Diffraction , 1971 .

[51]  Dirk Helm,et al.  Thermomechanical representation of the multiaxial behavior of shape memory alloys , 2002, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[52]  D. Lagoudas,et al.  A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy , 1996 .

[53]  L. Bocher,et al.  Experimental study of pseudoelastic behaviour of a Cu Zn AI polycrystalline shape memory alloy under tension-torsion proportional and non-proportional loading tests , 1996 .

[54]  D. McDowell,et al.  Mechanical behavior of an Ni-Ti shape memory alloy under axial-torsional proportional and , 1999 .

[55]  T. V. Tolpekina,et al.  Simulations of stable pores in membranes: system size dependence and line tension. , 2004, The Journal of chemical physics.

[56]  Alan E Mark,et al.  Simulation of pore formation in lipid bilayers by mechanical stress and electric fields. , 2003, Journal of the American Chemical Society.